Modelling negatives in stochastic reserving models

Kunkler, Michael

doi:10.1016/j.insmatheco.2005.11.006

Cited by 5 publications

(25 citation statements)

References 20 publications

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“…The earlier models such as de Alba (2002Alba ( , 2006 and Kunkler (2004Kunkler ( , 2006 are all aimed at solving the problem of loss reserving when either zeros or negatives appear in the loss triangle, but not both together. No model has been proposed for extending the stochastic reserving models to situations where there are both zeros and negatives existing in the loss triangle.…”

Section: A Bayesian Mixture Modelmentioning

confidence: 99%

“…Here, we will use notation consistent with that in Kunkler (2004Kunkler ( , 2006. Let y i j denote the incremental losses in the loss triangle.…”

Section: Distribution Of Mixture Datamentioning

confidence: 99%

“…So we can assume that the proportion of zeros and negatives depends only on the development year as in Kunkler (2004Kunkler ( , 2006. A Bayesian GLM for the multinomial probabilities on the development year j can be applied to model this structure.…”

Section: Generalized Linear Modelsmentioning

confidence: 99%

“…With a different factor δ ld introduced for each development year in the cumulative logistic model, the piecewise linear relationship (Kunkler, 2004(Kunkler, , 2006 gives a flexible structure. This model structure can be written as…”

Section: Generalized Linear Modelsmentioning

confidence: 99%

“…An improved Bayesian lognormal model was introduced by de Alba (2002,2006) to extend the lognormal model (Kremer, 1982) to situations where there are negative values in the loss triangle. Kunkler (2004Kunkler ( , 2006 proposed a Bayesian binomial model to handle the situation where there are either zeros or negatives in the loss triangle. None of these models, however, handle the more realistic situation when there are notable numbers of both zeros and negatives in the loss triangle.…”

Section: Introductionmentioning

confidence: 99%

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A Bayesian Mixture Model Accounting for Zeros and Negatives in the Loss Triangle

Xia

Scollnik²

2015

IJSP

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In insurance loss reserving, a large portion of zeros are expected at the later development periods of an incremental loss triangle. Negative losses occur frequently in the incremental loss triangle due to actuarial practices such as subrogation and salvation. The nature of the distributions assumed by most stochastic models, such as the lognormal and over-dispersed Poisson distributions, brings restrictions on the zeros and negatives appearing in the loss triangle. In this paper, we propose a Bayesian mixture model for stochastic reserving under the situation where there are both zeros and negatives in the incremental loss triangle. A multinomial regression model will be applied to model the sign of the loss data, while the lognormal distribution is assumed for the loss magnitudes of negatives and positives. Bayesian generalized linear models will be fitted for both the mixture and magnitude models. The model will be implemented using the Markov chain Monte Carlo (MCMC) techniques in BUGS. Our model provides a realistic tool for stochastic reserving in the cases of zeros and negatives.

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Section: A Bayesian Mixture Modelmentioning

confidence: 99%

“…Here, we will use notation consistent with that in Kunkler (2004Kunkler ( , 2006. Let y i j denote the incremental losses in the loss triangle.…”

Section: Distribution Of Mixture Datamentioning

confidence: 99%

Section: Generalized Linear Modelsmentioning

confidence: 99%

Section: Generalized Linear Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Bayesian Mixture Model Accounting for Zeros and Negatives in the Loss Triangle

Xia

Scollnik²

2015

IJSP

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Fast robust SUR with economical and actuarial applications

Hubert

Verdonck

Yorulmaz

2016

Statistical Analysis

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The seemingly unrelated regression (SUR) model is a generalization of a linear regression model consisting of more than one equation, where the error terms of these equations are contemporaneously correlated. The standard feasible generalized linear squares (FGLS) estimator is efficient as it takes into account the covariance structure of the errors, but it is also very sensitive to outliers. The robust SUR estimator of Bilodeau and Duchesne (Canadian Journal of Statistics, 28:277-288, 2000) can accommodate outliers, but it is hard to compute. First, we propose a fast algorithm, FastSUR, for its computation and show its good performance in a simulation study. We then provide diagnostics for outlier detection and illustrate them on a real dataset from economics. Next, we apply our FastSUR algorithm in the framework of stochastic loss reserving for general insurance. We focus on the general multivariate chain ladder (GMCL) model that employs SUR to estimate its parameters. Consequently, this multivariate stochastic reserving method takes into account the contemporaneous correlations among run-off triangles and allows structural connections between these triangles. We plug in our FastSUR algorithm into the GMCL model to obtain a robust version.

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Stochastic loss reserving with dependence: A flexible multivariate Tweedie approach

Avanzi

Taylor

et al. 2016

Insurance: Mathematics and Economics

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Stochastic loss reserving with dependence has received increased attention in the last decade. A number of parametric multivariate approaches have been developed to capture dependence between lines of business within an insurer's portfolio. Motivated by the richness of the Tweedie family of distributions, we propose a multivariate Tweedie approach to capture cell-wise dependence in loss reserving. This approach provides a transparent introduction of dependence through a common shock structure. In addition, it also has a number of ideal properties, including marginal flexibility, transparency, and tractability including moments that can be obtained in closed form. Theoretical results are illustrated using both simulated data sets and a real data set from a property-casualty insurer in the US.

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Modelling negatives in stochastic reserving models

Cited by 5 publications

References 20 publications

A Bayesian Mixture Model Accounting for Zeros and Negatives in the Loss Triangle

A Bayesian Mixture Model Accounting for Zeros and Negatives in the Loss Triangle

Fast robust SUR with economical and actuarial applications

Stochastic loss reserving with dependence: A flexible multivariate Tweedie approach

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